Optionally Q, U and V may or may not be computed, or they may be premultiplied by matrices Q1, U1 and V1 respectively.

If m-k-l≥0 then D1, D2 and R have the form

D1=klk(I0)l0Cm-k-l00,

D2=kll(0S)p-l00,

R=klk(R11R12)l0R22,

where C=diagαk+1,,,…,,,αk+l, S=diagβk+1,,,…,,,βk+l.

If m-k-l<0 then D1, D2 and R have the form

D1=km-kk+l-mk(I00)m-k0C0,

D2=km-kk+l-mm-k(0S0)k+l-m00Ip-l000,

R=km-kk+l-mk(R11R12R13)m-k0R22R23k+l-m00R33,

where C=diagαk+1,,,…,,,αm, S=diagβk+1,,,…,,,βm.

In both cases the diagonal matrix C has real non-negative diagonal elements, the diagonal matrix S has real positive diagonal elements, so that S is nonsingular, and C2+S2=1. See Section 2.3.5.3 of Anderson et al. (1999) for further information.

On exit: if m-k-l<0, Bm-k+1:l,n+m-k-l+1:n contains the submatrix R33 of R.

12: LDB – INTEGERInput

On entry: the first dimension of the array B as declared in the (sub)program from which F08YSF (ZTGSJA) is called.

Constraint:
LDB≥max1,P.

13: TOLA – REAL (KIND=nag_wp)Input

14: TOLB – REAL (KIND=nag_wp)Input

On entry: TOLA and TOLB are the convergence criteria for the Jacobi–Kogbetliantz iteration procedure. Generally, they should be the same as used in the preprocessing step performed by F08VSF (ZGGSVP), say